# Seminarios

## Futuros Eventos

2020-03-16
14:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Piotr Pokora. Pedagogical University of Cracow
Singular Curves and The Bounded Negativity Conjecture
Sala 2
Abstract:
In my talk I would like to present a brief introduction to the bounded negativity conjecture. This conjecture predicts that if $X$ is a smooth complex projective surface, then there exists an integer $b(X)$ such that for all reduced curves $C \subset X$ one always has $C^{2} \geq -b(X)$. This conjecture is widely open and we know that only for some types of surfaces the conjecture holds. In my talk I would like to focus on the most elementary case, namely the blow-ups of the complex projective plane. In the first part of my talk I would like to present some interesting constructions of curve arrangements which turns out to be very negative (as the strict transform) on the blow-ups. In the second part, I would like to present lower bounds of the so-called Harbourne constants which measure the local negativity phenomenon on algebraic surfaces.
My talk is based on the results obtained with many co-authors, but the core of the talk will follow from joint work with Joaquim Roé (Universidad Autonoma de Barcelona) and another subproject with Tomasz Szembeg (Pedagogical University of Kraków).

2020-03-04
14:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Eyal Goren. Mcgill University
Complex Multiplication - Old and New
Sala 1
Abstract:
The theory of complex multiplication is more than a century old; its origins date back to Klein, Hilbert, Kummer, Weber, Deuring and many others. It has been instrumental in the development of class field theory and algebraic number theory. Yet, more than a century later we find new theorems that are truly surprising.
I will start with this historical perspective and try to position some of these new developments in the light of the André-Oort conjecture - a conjecture in the area of Shimura varieties that was recently resolved by Tsimerman, building on ideas of Edixhoven, Pila, Wilkie and Zannier. The resolution rests on the averaged Colmez conjecture, a conjecture that addresses the arithmetic complexity of abelian varieties with complex multiplication, which was proved by Andreatta-Howard-Madapusi Pera and the speaker, and, independently, by Yuan-Zhang.

2020-01-29
12:00 hrs.
Seminario Núcleo Milenio Midas
José Quinlan. Pontificia Universidad Católica de Chile
On the Support of Yao-based Random Ordered Partitions for Change-Point Analysis
Abstract:

In Bayesian change-point analysis for univariate time series, prior distributions on the set of ordered partitions play a key role for change-point detection. In this context, mixtures of product partition models based on Yao's cohesion are very popular due to their tractability and simplicity. However, how flexible are these prior processes to describe different beliefs about the number and locations of change-points? In this talk I will address the previous question in terms of its weak support.

2020-01-22
10:00hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Diego Izquierdo. École Polytechnique
Lambda-buildings associated to quasi-split groups over Lambda-valued fields
Abstract:
Let $\Lambda$ be a totally ordered abelian group and let $K$ be a Henselian $\Lambda$-valued field. Let $G$ be a quasi-split reductive group over $K$. In 1972, Bruhat and Tits constructed a building on which the group $G(K)$ acts provided that $\Lambda$ is a subgroup of the real numbers. In this talk, we will deal with the general case where there are no assumptions on $\Lambda$ and construct a $\Lambda$-building in the sense of Bennett on which $G(K)$ acts.
Sala de seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-22
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Karim Johannes Becher. Universiteit Antwerpen
Abstract:
The interplay between valuations and certain geometrically rational varieties, in particular quadrics, has turned out to be very fruitful for proving that certain subsets of fields are existentially definable or diophantine. In particular, this has been used by J. Koenigsmann to prove that $\mathbb{Q}\backslash \mathbb{Z}$ is diophantine in $\mathbb{Q}$. His proof combines several ingredients from classical number theory, involving in particular the Hasse-Minkowski local-global principle for quadratic forms. In my talk I want to highlight some ingredients of proofs for showing that certain subsets of fields are diophantine and some interesting questions for quadratic forms arising from this context.
Sala de Seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-22
15:45 hrs.
Seminario Fismat
Some isoperimetric problems in the Euclidean space with density
Abstract:
We will discuss the isoperimetric problem for factorized measures obtained as perturbations of the Gaussian and the anti-Gaussian, respectively. Among other things, we will show that some isoperimetric problems, for which balls centered at the origin are stable, have no solutions.Time permitting, some applications, like, for instance, Faber-Krahn type inequalities will be presented too. (Joint works with F. Brock and A. Mercaldo)
2020-01-22
12:00 hrs.
Seminario Núcleo Milenio Midas
Miles Ott. Smith College
Respondent-Driven Sampling: Challenges and Opportunities
Abstract:
Respondent-driven sampling leverages social networks to sample hard-to-reach human populations, including among those who inject drugs, sexual minority, sex worker, and migrant populations.  As with other link-tracing sampling strategies, sampling involves recruiting a small convenience sample, who invite their contacts into the sample, and in turn invite their contacts until the desired sample size is reached. Typically, the sample is used to estimate prevalence, though multivariable analyses of data collected through respondent-driven sampling are becoming more common. Although respondent-driven sampling may allow for quickly attaining large and varied samples, its reliance on social network contacts, participant recruitment decisions, and self-report of ego-network size makes it subject to several concerns for statistical inference.  After introducing respondent-driven sampling I will discuss how these data are actually being collected and analyzed, and opportunities for statisticians to improve upon this widely-adopted method.
2020-01-21
16:00hrshrs.
Seminario de Análisis y Geometría
Barbara Brandolini. Departamento de Matemáticas, Universidad de Nápoles, Italia
Improved bounds for Hermite-Hadamard inequalities in higher dimensions
Abstract:
ver pdf
2020-01-15
12:00 hrs.
Seminario Núcleo Milenio Midas
Nicolas Kuschinski. Pontificia Universidad Católica de Chile
FATSO: Una familia de operadores para selección de variables en modelos lineales
Abstract:
En modelos lineales es común encontrarse con situaciones donde varios de los coeficientes de regresión son 0. En estas situaciones, una herramienta común es un operador de selección de variables de tipo "sparsity promoting". El más común de estos operadores es el LASSO, el cual promueve estimaciones en 0. Sin embargo, el LASSO y sus derivados dan poco en términos de parámetros fácilmente interpretables para controlar el grado de selectividad. En esta plática se propondrá una nueva familia de operadores de selección, la cual toma como base la geometría del LASSO, pero que tienen forma analítica distinta, y que dan una manera fácilmente interpretable de controlar el grado de selectividad. Estos operadores corresponden con densidades a priori propias, y por ende se pueden usar para hacer inferencia Bayesiana.
2020-01-14
14:30hrs.
Santiago Number Theory and Algebra Seminar (Santas)
Chao Li. Columbia University
On the Kudla-Rapoport conjecture
Abstract:
The classical Siegel-Weil formula relates certain Siegel Eisenstein series with quadratic forms, namely expressing special values of these series as theta functions --- generating series of representation numbers of quadratic forms. The influential program of Kudla aims to establish the arithmetic Siegel-Weil formula, which relates the derivative of certain Siegel Eisenstein series with generating series from arithmetic geometry. We will report a proof of the Kudla-Rapoport conjecture, and discuss its application to L-functions such as generalizations of the Gross-Zagier formula to higher dimension. This is joint work with Wei Zhang.
Sala de Seminarios, Dpto de Matemáticas. Las Palmeras 3425, Universidad de Chile
2020-01-10
14:00hrs.
Seminario de Teoría de Números
Chao Li. Columbia University
Elliptic curves and Goldfeld's conjecture
Abstract:

An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which lead to the celebrated conjecture of Birch and Swinnerton-Dyer. Within a family of elliptic curves (such as the Mordell curve family $y^2=x^3+d$), a conjecture of Goldfeld further predicts that there should be infinitely many rational solutions exactly half of the time. We will start with a history of this problem, discuss our joint work with D. Kriz towards Goldfeld's conjecture and illustrate the key ideas and ingredients behind these new progresses.

Sala 2
2020-01-08
14:00hrs.
Seminario de Geometría Algebraica
Luca Schaffler. University of Massachusetts At Amherst
Compactifications of moduli spaces of algebraic varieties
Abstract:
In algebraic geometry, an algebraic variety is a geometric object defined
by polynomial equations. The space of parameters for a family of algebraic
varieties may also be an algebraic variety called a moduli space. In this
talk oriented to a general audience, I will motivate the study of
compactifications of moduli spaces, focusing on the case of moduli of
polarized K3 surfaces. The original results (joint works with Moon and
Gallardo-Kerr) concern the study of a family of K3 surfaces arising from
eight points in the projective line, and the interplay between different
compactifications of such family coming from Geometric Invariant Theory,
Hodge Theory, and the Minimal Model Program.
sala 2